Sampling of an analog electric signal consists of both time discretization and amplitude discretization of a time-invariant signal, i.e. a voltage or current.
A simple representation of a sampling operation is a switch, which at a certain rate, i.e. the sampling rate, permits transfer of the analog signal during a short time relative to the sampling period. The thus sampled analog signal than consists of short segments or sample values of the analog signal having an amplitude which corresponds to the amplitude of the analog signal at the time of sampling.
The sampling operation can be represented as a multiplication of the analog signal and a periodic pulse train, the period of which is the sampling rate.
It can be shown that such multiplication operation, in the frequency domain, results in a spectrum of signals comprising the spectrum of the sampled analog signal and a periodic repetition of the spectrum with a spacing determined by the sampling rate and having a decreasing spectral power. The attenuation is determined by the sampling process, i.e. the duration and the amplitude of the pulses of the periodic pulse train and the sampling rate.
The minimum sampling rate at which no overlap of the repeated analog signal is encountered, is called the nominal Nyquist rate. That is, the minimum sampling frequency has to be at least twice the upper frequency of a frequency band limited signal.
A more elaborated discussion on sampling can be found in many textbooks dealing with electric communication such as "Communication Systems", by A. Bruce Carlson, McGraw-Hill 1975, second edition Chapter 8.
In practice, real analog signals are not strictly band limited, such that whenever frequencies occur in the analog signal which are undersampled, that is the Nyquist criterion is not met for such frequencies, a phenomenon occurs which is called aliasing. With aliasing spectral overlap of repeated spectra occurs, such that after reconstruction of the sampled signal, frequencies which were originally outside the frequency band of the sampled signal will now appear at the reconstructed output in the form of lower frequencies, distorting the reconstructed sampled analog signal.
Aliasing is combatted by removing or filtering as much as possible frequency components above the frequency band of the signal to be sampled before the actual sampling thereof and, if possible, sampling at a much higher rate than the nominal Nyquist rate. Such type of filtering is also called anti-aliasing filtering. Reference is made to European patent application 0,335,037.
In practice, there is a compromise between the order of the filter, i.e. a Low Pass (LP) or a Band Pass (BP) filter and the sample rate which may relate to the conversion speed of an Analog-to-Digital Converter (ADC) used, and thus its power consumption.